I do get erratic behavior with the cover...
So the cover may be goofing up the Glo. My cover springs open about 1/8" - just enough to turn the Glo back on again, and when lying flat on its back without the rubber band, it sometimes goes back and forth between On and Off. I'm guessing that it might be provoking a bug, by being turned On when it is in the process of going to sleep, or something similar.
Try setting it down with the screen side down instead of up, so the cover is held firmly closed by the weight of the Glo, and see if the cover still causes the problem.